Mathematics Made Easy for Children with Visual Impairment - ICEVI

364 Pages·2008·5.3 MB·English

PROJECT DEVELOPMENT TEAM
Dr. M.N.G. Mani, Co-chair Aree Plernchaivanich, Co-chair
Secretary General, ICEVI Head of the Center
IHRDC Campus Special Education Center Region 7
Ramakrishna Mission Vidyalaya Tambol Thatthong, Amphur Muang
Coimbatore - 641 020 Phitsanulok
INDIA THAILAND
[email protected] [email protected]
G.R. Ramesh Larry Campbell
Lecturer in Special Education President - ICEVI
IHRDC Overbrook School for the Blind
Ramakrishna Mission Vidyalaya 6333 Malvern Avenue
Coimbatore 641 020 Philadelphia, PA 19151-2597
INDIA USA
[email protected] [email protected]
DEDICATION
This publication is dedicated to Mr. Yohei Sasakawa and The Nippon Foundation
whose belief in the capabilities of persons with visual impairment has allowed
them, their parents and their teachers from throughout Southeast Asia to work
together to make this project and this publication a reality.
Message from the Director
Overbrook School for the Blind
Overbrook is proud to release this publication with our colleagues at the International Council
for Education of People with Visual Impairment (ICEVI) and we hope you will find it of value
in strengthening your ability to teach secondary level mathematics concepts to children with
visual impairment.
For as long as I have been involved in the education of children with visual impairment, the
teaching of mathematics has been a persistent challenge facing educators here in the United
States. As you read the introduction to this publications you will note that this is a challenge
facing many countries throughout the world. We hope this publication will be of assistance
to teachers, parents and students wherever they live in improving mathematics instruction.
Through our International Program here at Overbrook and our collaboration with The Nippon
Foundation (Japan) we have been able to work with a very talented and dedicated project
development team in creating this resource. Through this team we have been able to work
with hundreds of teachers in the Asia region to respond to this challenge and to develop this
publication. To all of these individual we express our thanks for their contributions.
We sincerely hope that this publication will assist countless children with visual impairment
throughout the world to master secondary level mathematics by providing their teachers and
parents with a resource that will improve instructional strategies.
As with all publications, we value your feedback. Both Overbrook and ICEVI look forward
to your comments on this publication.
Sincerely,
Bernadette M. Kappen, Ph.D.
Director
CONTENTS
Introduction 1
Section 1
Methodology of Teaching Mathematics
Module 1 : Approaches in Learning Mathematics 11
Module 2 : Improvisation of Teaching Aids in Mathematics 16
Module 3 : Mathematics in Integrated Classrooms 21
Section 2
Use of Abacus
Module 4 : Abacus - General Concepts 25
Module 5 : Pre-requisite skills for the efficient learning of Abacus 28
Module 6 : Abacus - Addition 29
Module 7 : Abacus - Subtraction 33
Module 8 : Abacus - Multiplication 35
Module 9 : Abacus - Multiplication of two digit numbers 38
Module 10 : Abacus - Multiplication involving zero 40
Module 11 : Abacus - Division 43
Module 12 : Abacus - Long Division 45
Module 13 : Abacus Division - Quotient and Remainder 49
Module 14 : Abacus - Decimal Addition 51
Module 15 : Abacus - Subtraction of Decimals 53
Module 16 : Abacus - Multiplication of Decimals 54
Module 17 : Abacus - Division of Decimals 55
Module 18 : Abacus - Fraction Attraction 56
Module 19 : Abacus - Fraction Subtraction 60
Module 20 : Abacus - Fraction Multiplication 63
Module 21 : Abacus - Division of Fractions 68
Module 22 : Abacus - Square Root 70
Module 23 : Abacus - Square root of multiple digit numbers 74
Module 24 : Abacus - Square root of imperfect square 76
Module 25 : Abacus - Percentage 78
Section 3
Use of Nemeth Mathematical Braille Codes
Modules 26 - 50 81
Section 4
Instructional Strategies
Module 51 : General Concepts 118
Module 52 : Numbers 133
Module 53 : Rational Numbers 147
Module 54 : Four Fundamental Operations 149
Module 55 : Tests of Divisibility 152
Module 56 : Decimals 154
Module 57 : Percentage 162
Module 58 : Fractions 165
Module 59 : Measures of Area 171
Module 60 : Measures of Volume 177
Module 61 : Measure of Time 178
Module 62 : Radicals 180
Module 63 : Algebraic Concepts 183
Module 64 : Laws of Indices 196
Module 65 : Algebraic Identities 198
Module 66 : Polynomials 200
Module 67 : Factorization 208
Module 68 : Logarithm 221
Module 69 : Geometry - Circle 223
Module 70 : Angles 231
Module 71 : Triangles 238
Module 72 : Quadrilaterals 244
Module 73 : Simple Interest 250
Module 74 : Sets 255
Module 75 : Venn Diagram 267
Module 76 : Relations 271
Module 77 : Functions 273
Module 78 : Binary System 280
Module 79 : Matrices 284
Module 80 : Rectangular Coordinate System 294
Module 81 : Trigonometry 297
Module 82 : Analytical Geometry 302
Module 83 : Statistics 311
Module 84 : Probability 324
Section 5
Module 85 : Creative Mathematics 329
Module 86 : Angles 331
Module 87 : Circles 336
Module 88 : Triangle 340
Module 89 : Quadrilaterals 345
Module 90 : Identities 347
1
INTRODUCTION
ON-NET / ICEVI MATHEMATICS PROJECT
THE EVOLUTION OF THIS PUBLICATION
SETTING THE SCENE
In July, 1998 the Overbrook School for the Blind (USA) and The Nippon Foundation (Japan)
embarked on a unique and ambitious collaborative effort to improve and expand education
and employment opportunities for blind persons in Southeast Asia. The program set out to
address needs of blind and low vision persons in eight (8) countries in Southeast Asia
(Cambodia, Indonesia, Laos, Malaysia, Myanmar, Philippines, Thailand and Vietnam).
The program was created on the assumption that with: -collaboration at the national and
regional levels, -effective use of new technologies and -active involvement of blind
individuals, their organizations, teachers and parents would result in improved educational
access for blind children and youth and new employment options for educated blind adults.
This program, the Overbrook-Nippon Network on Educational Technology, soon became
better known by its acronym ON-NET.
In addition to ON-NET national level committees that set the tone and priorities for each
country, ON-NET also created a Regional Advisory Committee whose task was to identify
challenges that were: -common to all or most of the countries in the region and -might be
most effectively addressed through a region strategy.
At the first ON-NET Regional Advisory Committee meeting in December, 2001 the issue of
weak instruction in mathematics for blind children was identified as one of several priorities
that might best be tackled through a well planned regional strategy. This same group noted
that poor instruction in the area was a region-wide weakness and that it was placing
2
significant impediments in the career path of otherwise well educated blind persons who
wanted to pursue careers in the areas of science and technology.
As is the case with most challenges, it is always easier to identify a problem than it is to
create a solution. However, in January, 2003 a group of teachers, blind individuals, teacher
trainers and members of the ON-NET Regional Advisory Group met in Bangkok and agreed
that a plan to prepare a small but very carefully selected group of Master Trainers from
throughout the region was something worth doing. It was further agreed that while
mathematics instruction at all levels was weak; our focus should be on improving secondary
level mathematics instruction for the blind.
In May, 2003 a group of experts met at the ON-NET Regional Center at Ratchasuda College
of Mahidol University to work out the details of putting together an expert team to conduct
the Master Trainers program and to a comprehensive mathematical package that could be
field-tested and then used by the Master Trainers to train others. This publication is the
result of that effort over the past three years.
At the Bangkok planning meeting, I invited Dr. M.N.G. Mani, Secretary General, ICEVI and
Ms. Aree Plernchaivanich, Director, Region 7 Special Education Center, Phitsanuloke, Thailand
to co-chair a Math Task Force that would develop the training program and the training
materials. Both Dr. Mani and Ms. Plernchaivanich are experienced educators of children
with visual impairment and mathematics teachers. Mr. G.R. Ramesh, Lecturer in Special
Education, International Human Resource Development Center for the Disabled, Ramakrishna
Mission Vidalaya, Coimbatore, India was later co-opted to the Task Force.
There was unanimous agreement that developing a learning package for teaching mathematics
would not only facilitate improved ability of special educators teaching mathematics to
blind children, but the materials would also be useful for general classroom teachers as
well.
Next, the group tackled the question of where to begin. There was agreement that some of
the background materials such as use of abacus, creative mathematics, easy ways of teaching
Nemeth code, etc., developed by Dr. Mani in training teachers of mathematics would form
an excellent base for the learning package. Following a series of deliberations by Dr. Mani,
Ms. Plernchaivanich, Mr. Ramesh and myself during May and June 2003, it was decided to
develop a mathematics package that would address the following major areas: